{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "首先说明一下，这一节其实与EM没多大关系，只是想对GMM的分类作一个实现并推导它与LogisticRegression之间的关系\n",
    "### 一.分类原理\n",
    "分类实现的原理非常简单，对每一个类训练一个高斯模型模型（如果你喜欢，多个也是可以的，这里你就可以使用用EM算法了，将前面的GMMCluster简单封装一下就可以）即可，然后每个类的权重由其样本所占比例确定"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir('../')\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from ml_models.em import GMMCluster\n",
    "\n",
    "\"\"\"\n",
    "利用GMMCluster实现分类，代码封装到ml_models.em\n",
    "\"\"\"\n",
    "\n",
    "class GMMClassifier(object):\n",
    "    def __init__(self, cluster_each_class=1, n_iter=100, tol=1e-3, shr_cov=False):\n",
    "        \"\"\"\n",
    "        :param cluster_each_class:每个类需要几个高斯模型去拟合，默认1个\n",
    "        :param n_iter:迭代次数\n",
    "        :param tol: -log likehold增益<tol时，停止训练\n",
    "        :param shr_cov:是否共享协方差矩阵\n",
    "        \"\"\"\n",
    "        self.cluster_each_class = cluster_each_class\n",
    "        self.n_iter = n_iter\n",
    "        self.tol = tol\n",
    "        self.shr_cov = shr_cov\n",
    "        self.models = []\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        for y_index in range(y.max() + 1):\n",
    "            new_X = X[y == y_index]\n",
    "            cluster = GMMCluster(n_components=self.cluster_each_class, tol=self.tol, n_iter=self.n_iter)\n",
    "            cluster.fit(new_X)\n",
    "            self.models.append(cluster)\n",
    "        if self.shr_cov:\n",
    "            # 获取所有的协方差矩阵\n",
    "            sigmas = []\n",
    "            for model in self.models:\n",
    "                params = model.params\n",
    "                for param in params:\n",
    "                    sigmas.append(param[2])\n",
    "            # 求平均\n",
    "            ave_sigma = np.mean(sigmas, axis=0)\n",
    "            # 更新\n",
    "            for model in self.models:\n",
    "                params = model.params\n",
    "                for param in params:\n",
    "                    param[2] = ave_sigma\n",
    "\n",
    "    def predict_proba(self, X):\n",
    "        W = np.asarray([model.predict_sample_generate_proba(X) for model in self.models]).T\n",
    "        W = W / np.sum(W, axis=1, keepdims=True)\n",
    "        return W\n",
    "\n",
    "    def predict(self, X):\n",
    "        return np.argmax(self.predict_proba(X), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\deprecation.py:144: FutureWarning: The sklearn.datasets.samples_generator module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "#造数据\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "from ml_models import utils\n",
    "\n",
    "X, y = make_blobs(n_samples=400, centers=4, cluster_std=0.85, random_state=0)\n",
    "X = X[:, ::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#训练模型并可视化\n",
    "gmm = GMMClassifier(n_iter=100)\n",
    "gmm.fit(X, y)\n",
    "utils.plot_decision_function(X, y, gmm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "代码里面添加了一个`shr_cov`的超参，如果`shr_cov=True`表示所有的模型都会共享同一个协方差矩阵，我们接下来看看会发生什么"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GMMClassifier(n_iter=100,shr_cov=True)\n",
    "gmm.fit(X, y)\n",
    "utils.plot_decision_function(X, y, gmm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现类与类的边界都变成了**直线**，这时的GMM模型似乎退化成了一个线性模型，这是为什么呢？它这时其实是一个带有一定约束的LogisticRegression模型，接下来我们推推看它们之间的关系"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二.协方差矩阵共享的GMM模型与LogisticRegression的关系\n",
    "以二分类为例进行推导，假如我们训练好了两个分类模型，分别为$C_1,C_2$，那么有：   \n",
    "\n",
    "$$\n",
    "p(x\\mid C_1)=N(x\\mid u_1,\\Sigma)\\\\\n",
    "p(x\\mid C_2)=N(x\\mid u_2,\\Sigma)\\\\\n",
    "p(C_1)+p(C_2)=1\n",
    "$$   \n",
    "所以，高斯混合模型：   \n",
    "\n",
    "$$\n",
    "p(x)=p(C_1)p(x\\mid C_1)+p(C_2)p(x\\mid C_2)\n",
    "$$  \n",
    "\n",
    "接下来，我们转换为判断模型的形式：   \n",
    "\n",
    "$$\n",
    "p(C_1\\mid x)=\\frac{p(C_1)p(x\\mid C_1)}{p(x)}\\\\\n",
    "=\\frac{p(C_1)p(x\\mid C_1)}{p(C_1)p(x\\mid C_1)+p(C_2)p(x\\mid C_2)}\\\\\n",
    "=\\frac{1}{1+exp(-Z)}\n",
    "$$   \n",
    "\n",
    "这里$Z=log\\frac{p(C_1)p(x\\mid C_1)}{p(C_2)p(x\\mid C_2)}$，这里已经看到了LogisticRegression的雏形了，接着，我们将$Z$化简看看：  \n",
    "\n",
    "$$\n",
    "Z=log\\frac{p(C_1)p(x\\mid C_1)}{p(C_2)p(x\\mid C_2)}\\\\\n",
    "=log\\frac{p(x\\mid C_1)}{p(x\\mid C_2)}+log\\frac{p(C_1)}{p(C_2)}\\\\\n",
    "=....省略....\\\\\n",
    "=(u_1-u_2)^T\\Sigma^{-1}x-\\frac{1}{2}u_1^T\\Sigma^{-1}u_1+\\frac{1}{2}u_2^T\\Sigma^{-1}u_2+log\\frac{N_1}{N_2}(N_1,N_2表示1,2类的样本量\\frac{p(C_1)}{p(C_2)}=\\frac{N_1}{N_2})\n",
    "$$  \n",
    "\n",
    "所以，如果令：  \n",
    "$$\n",
    "w^T=(u_1-u_2)^T\\Sigma^{-1}\\\\\n",
    "b=-\\frac{1}{2}u_1^T\\Sigma^{-1}u_1+\\frac{1}{2}u_2^T\\Sigma^{-1}u_2+log\\frac{N_1}{N_2}\n",
    "$$  \n",
    "\n",
    "那么：  \n",
    "\n",
    "$$\n",
    "Z=w^Tx+b\n",
    "$$  \n",
    "\n",
    "那么：  \n",
    "\n",
    "$$\n",
    "p(C_1\\mid x)=\\frac{1}{1+exp(-w^Tx-b)}\n",
    "$$  \n",
    "\n",
    "所以，如果数据量大没必要去训练一个复杂的GMM分类器，就训练一个LR就好啦..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
